The present invention relates to prism optical systems including a reflecting surface that is decentered and has a power, for example, a prism optical system for use in an image-forming optical system, a finder optical system, etc. used in cameras, video cameras and so forth.
Recently, there have been proposed optical systems designed to be compact in size by giving a power to a reflecting surface and folding an optical path in the direction of the optical axis. In such optical systems, a prism or a mirror is mainly used as a member having a reflecting surface with a power. An optical system having a prism and an optical system having a mirror are largely different in characteristics from each other although these optical systems are the same in terms of the structure using a reflecting surface.
When a curvature (radius r of curvature) is given to a reflecting surface of a prism and to a reflecting surface of a mirror, the power of each of the reflecting surfaces is given by the paraxial power calculating equation as follows. The power of the reflecting surface of the prism is xe2x88x922n/r in a case where the prism is filled therein with a medium having a refractive index n larger than 1, whereas the power of the reflecting surface of the mirror is xe2x88x922/r. Thus, even when these reflecting surfaces have the same curvature, the powers are different from each other. Accordingly, the curvature required for the prism is 1/n of the curvature required for the mirror to obtain the same power. Therefore, the prism produces a smaller amount of aberration at the reflecting surface than in the case of the mirror. Thus, the prism is more favorable than the mirror in terms of performance. Moreover, the prism has two refracting surfaces, i.e. an entrance refracting surface and an exit refracting surface, in addition to a reflecting surface as a single member. Therefore, the prism is advantageous from the viewpoint of aberration correction in comparison to the mirror, which has only a reflecting surface as a single member. Furthermore, because the prism is filled with a medium having a refractive index larger than 1, it is possible to obtain a longer optical path length than in the case of the mirror, which is placed in the air. Accordingly, it is relatively easy with the prism to provide the required reflecting surface even when the focal length is short. In general, reflecting surfaces require a high degree of accuracy for assembly because decentration errors of reflecting surfaces cause the performance to be degraded to a considerable extent in comparison to refracting surfaces. In a case where an optical system is constructed by arranging a plurality of reflecting surfaces, the prism is more advantageous than the mirror because the prism enables a plurality of reflecting surfaces to be integrated into one unit so as to fix the relative positions and is therefore capable of preventing performance degradation due to assembling. Thus, the prism is superior to the mirror in many respects.
Meanwhile, when a surface with a power is placed at a tilt to the optical axis, rotationally asymmetric aberrations are produced. For example, if a rotationally asymmetric distortion occurs, a square object may become trapezoidal undesirably. Such rotationally asymmetric aberrations (hereinafter referred to as xe2x80x9cdecentration aberrationsxe2x80x9d) are impossible to correct by a rotationally symmetric surface in theory. For this reason, rotationally asymmetric curved surfaces, e.g. anamorphic surfaces, are used in conventional prism optical systems.
Such prism optical systems include the disclosure of Japanese Patent Application Unexamined Publication (KOKAI) Number [hereinafter referred to as xe2x80x9cJP(A)xe2x80x9d]8-313829. JP(A) 8-313829 discloses an ocular optical system comprising a prism in which there are two reflections, and a first transmitting surface and a second reflecting surface, as counted from the pupil side, are formed from the identical surface. In this optical system, all reflecting surfaces are rotationally asymmetric anamorphic surfaces.
Among the conventional prism optical systems using rotationally asymmetric curved surfaces, prism optical systems in which there are three reflections, in particular, are disclosed in JP(A) 9-33855, 9-73043 and 9-197336. These optical systems use spherical or anamorphic surfaces as reflecting surfaces.
JP(A) 9-33855 discloses an ocular optical system in which an optical axis thereof forms an optical path that makes one turn in the prism. A third reflecting surface and a first transmitting surface, as counted from the pupil side, are formed from the identical surface, and a second reflecting surface and a second transmitting surface are formed from the identical surface. The prism optical system has only one reflecting surface that is independent of other transmitting and reflecting surfaces, i.e. the second reflecting surface. The direction in which light exits from the prism optical system is about 45 degrees oblique to the direction in which light enters the prism optical system.
JP(A) 9-73043 discloses an ocular optical system in which an optical axis thereof forms an M-shaped optical path. In Example 5 of JP(A) 9-73043, for instance, a second reflecting surface and a second transmitting surface, as counted from the pupil side, are formed from the identical surface. The prism optical system has only two surfaces that are independent of other transmitting and reflecting surfaces, i.e. a first reflecting surface and a third reflecting surface. In this example, the direction in which light exits from the prism optical system is opposite to the direction in which light enters the optical system. In JP(A) 9-197336, which has an arrangement similar to the above, a second reflecting surface, as counted from the pupil side, is formed from the identical surface with a first transmitting surface and a second transmitting surface.
These prior art prism optical systems suffer, however, from various problems as stated below.
In JP(A) 8-313829, the reflecting surfaces of the prism are given a power. However, because the prism optical system has only two reflecting surfaces, there is a limit in achieving high performance. If the aperture becomes large or the field angle becomes large, the optical system may fail to fulfill the required performance.
Accordingly, it is conceivable to increase the number of reflections so that aberration correction can be made even more effectively. However, a reduction in size and an increase in performance cannot simultaneously be attained in all the prior art prism optical systems in which there are three reflections, that is, the number of reflections is larger than that in the above-described prior art prism optical system by one.
In JP(A) 9-33855, the optical path is arranged to turn in the prism. Therefore, a reduction in size of the prism can be attained effectively by folding the optical path. However, as the light beam becomes large, it is difficult to form two transmitting surfaces and three reflecting surfaces by using independent surfaces, respectively, owing to the structure thereof. Therefore, it is inevitably necessary to form the first transmitting surface and the third reflecting surface from the identical surface and to form the second transmitting surface and the first transmitting surface from the identical surface. Consequently, the angle of reflection at each of the first and third reflecting surfaces needs to be not less than the total reflection critical angle. Therefore, aberration correction cannot satisfactorily be effected. In addition, because the angle of reflection is limited at two of the three reflecting surfaces, there is almost no freedom for the exit direction with respect to the entrance direction. Therefore, considering placement of another member, there are cases where it is impossible to achieve a reduction in size of the prism optical system.
In JP(A) 9-73043 and 9-197336, the prism optical system has an M-shaped optical path. Therefore, the second reflecting surface is likely to overlap the effective portion of a light beam passing through either or both of the first and second transmitting surfaces. Accordingly, the second reflecting surface unavoidably needs to be formed from the identical surface with either or both of the first and second transmitting surfaces. For this reason, the angle of reflection at the second reflecting surface needs to be not less than the total reflection critical angle as in the case of the above. Consequently, satisfactory aberration correction cannot be effected. In addition, because the exit direction is nearly parallel to the entrance direction, if the back focus is increased, or if another optical system is connected to the prism optical system, the resulting optical system becomes undesirably large in size in the entrance direction. Therefore, there are cases where it is impossible to achieve a reduction in size of the optical system.
Thus, all the prior art prism optical systems involve problems in terms of performance or size. There has heretofore been no compact and high-performance prism optical system that satisfies the demand for an improvement in performance and the demand for a reduction in size at the same time.
In view of the above-described problems associated with the prior art, an object of the present invention is to provide a compact and high-performance prism optical system.
A prism optical system according to the present invention provided to attain the above-described object has, in order in which light rays pass from the object side, a first transmitting surface, a first reflecting surface, a second reflecting surface, a third reflecting surface, and a second transmitting surface. When an axial principal ray is projected onto a plane defined by three points at which the axial principal ray impinges on the first transmitting surface, the first reflecting surface and the second reflecting surface, the projected axial principal ray forms an optical path that bends at two consecutive reflecting surfaces in the same direction with respect to the direction of travel of the rays and bends at the other reflecting surface in a direction different from the direction of bending at the two reflecting surfaces. At least one of the three reflecting surfaces is a rotationally asymmetric surface.
Another prism optical system according to the present invention has, in order in which light rays pass from the object side, a first transmitting surface, a first reflecting surface, a second reflecting surface, a third reflecting surface, and a second transmitting surface. When an axial principal ray is projected onto a plane defined by three points at which the axial principal ray impinges on the first transmitting surface, the first reflecting surface and the second reflecting surface, the projected axial principal ray forms an optical path that bends at the first and second reflecting surfaces in the same direction with respect to the direction of travel of the rays and bends at the third reflecting surface in a direction different from the direction of bending at the first and second reflecting surfaces. At least one of the three reflecting surfaces is a rotationally asymmetric surface.
Still another prism optical system according to the present invention has, in order in which light rays pass from the object side, a first transmitting surface, a first reflecting surface, a second reflecting surface, a third reflecting surface, and a second transmitting surface. When an axial principal ray is projected onto a plane defined by three points at which the axial principal ray impinges on the first transmitting surface, the first reflecting surface and the second reflecting surface, the projected axial principal ray forms an optical path that bends at the second and third reflecting surfaces in the same direction with respect to the direction of travel of the rays and bends at the first reflecting surface in a direction different from the direction of bending at the second and third reflecting surfaces. At least one of the three reflecting surfaces is a rotationally asymmetric surface.
A further prism optical system according to the present invention has three prism reflecting surfaces placed between an aperture of the prism optical system and an object plane or an image plane. The prism optical system has, in order in which light rays pass from the object side, a first transmitting surface, a first reflecting surface, and a second reflecting surface. When an axial principal ray is projected onto a plane defined by three points at which the axial principal ray impinges on the first transmitting surface, the first reflecting surface and the second reflecting surface, the projected axial principal ray forms an optical path that bends at two consecutive reflecting surfaces in the same direction with respect to the direction of travel of the rays and bends at the other reflecting surface in a direction different from the direction of bending at the two reflecting surfaces. At least one of the three reflecting surfaces is a rotationally asymmetric surface.
The reasons for adopting the above-described arrangements in the present invention, together with the functions thereof, will be described below.
As has been stated in regard to the prior art, if a reflecting surface is tilted with respect to the optical axis, rotationally asymmetric decentration aberrations are produced. Therefore, it is desirable that at least one reflecting surface of the surfaces used in the present invention should be a rotationally asymmetric surface. If a rotationally asymmetric surface is used as at least one reflecting surface, it becomes possible to correct the rotationally asymmetric decentration aberrations.
Let us explain the definition of a decentered system.
First, a coordinate system used in the following description and rotationally asymmetric surfaces will be described.
When a light ray from the object center that passes through the center of the stop and reaches the center of the image plane is defined as an axial principal ray, an optical axis defined by a straight line along which the axial principal ray travels until it intersects the first surface of the optical system is defined as a Z-axis. An axis perpendicularly intersecting the Z-axis in the decentration plane of each surface constituting the prism optical system is defined as a Y-axis. An axis perpendicularly intersecting the optical axis and also perpendicularly intersecting the Y-axis is defined as an X-axis. In the following description, ray tracing is forward ray tracing in which rays are traced from the object toward the image plane.
The rotationally asymmetric surface used in the present invention should preferably be a plane-symmetry free-form surface having only one plane of symmetry.
Free-form surfaces used in the present invention are defined by the following equation (A).
Z=C2X+C3Y+C4X2+C5XY+C6Y2+
C7X3+C8X2Y+C9XY2+C10Y3+C11X4+C12X3Y+C13X2Y2+C14XY3+C15Y4+
C16X5+C17X4Y+C18X3Y2+C19X2Y3+C20XY4+C21Y5+C22X6+C23X5Y+
C24X4Y2+C25X3Y3+C26X2Y4+C27XY5+C28Y6+C29X7+C30X6Y+
C31X5Y2+C32X4Y3+C33X3Y4+C34X2Y5+C35XY6+C36Y7xe2x80x83xe2x80x83(A)
In general, the above-described free-form surface does not have planes of symmetry in both the XZ- and YZ-planes. In the present invention, however, a free-form surface having only one plane of symmetry parallel to the YZ-plane is obtained by making all terms of odd-numbered degrees with respect to X zero. For example, in the above defining equation (A), the coefficients of the terms C2, C5, C7, C9, C12, C14, C16, C18, C20, C23, C25, C27, C29, C31, C33, C35, . . . are set equal to zero. By doing so, it is possible to obtain a free-form surface having only one plane of symmetry parallel to the YZ-plane.
A free-form surface having only one plane of symmetry parallel to the XZ-plane is obtained by making all terms of odd-numbered degrees with respect to Y zero. For example, in the above defining equation (A), the coefficients of the terms C3, C5, C8, C10, C12, C14, C17, C19, C21, C23, C25, C27, C30, C32, C34, C36, . . . are set equal to zero. By doing so, it is possible to obtain a free-form surface having only one plane of symmetry parallel to the XZ-plane.
Furthermore, the direction of decentration is determined in correspondence to either of the directions of the above-described planes of symmetry. For example, with respect to the plane of symmetry parallel to the YZ-plane, the direction of decentration of the optical system is determined to be the Y-axis direction. With respect to the plane of symmetry parallel to the XZ-plane, the direction of decentration of the optical system is determined to be the X-axis direction. By doing so, rotationally asymmetric aberrations due to decentration can be corrected effectively, and at the same time, productivity can be improved.
It should be noted that the above defining equation is shown as merely an example, and that the feature of the present invention resides in that rotationally asymmetric aberrations due to decentration are corrected and, at the same time, productivity is improved by using a rotationally asymmetric surface having only one plane of symmetry. Therefore, the same advantageous effect can be obtained for any other defining equation that expresses such a rotationally asymmetric surface.
It becomes possible to correct decentration aberrations by using such a rotationally asymmetric surface. However, if the number of aberration correcting surfaces is small, the increase in performance is limited even if rotationally asymmetric surfaces are used. Therefore, increasing the number of reflecting surfaces of the prism optical system is favorable from the viewpoint of performance.
However, simply increasing the number of reflecting surfaces of the prism is not always favorable for performance. The prism generally needs to fold light rays so that the effective portions of the reflecting surfaces do not overlap each other. Therefore, when there are a surface a, a surface b, and a surface c in order in which rays pass, for example, it is necessary to increase the angle of reflection at the surface b or to increase the spacing between the surfaces a and b and the spacing between the surfaces b and c so that the effective portions of these surfaces do not overlap each other. The amount of decentration aberrations produced by a reflecting surface generally becomes larger as the angle of reflection at the surface increases. Therefore, increasing the reflection angle is unfavorable for performance. If the spacing between the reflecting surfaces is increased, it becomes necessary to increase the optical path length. Consequently, the load of ensuring the required performance becomes unfavorably heavy, and the prism also becomes unfavorably large in size.
In a case where the effective portions undesirably overlap each other as stated above, it is conceivable to adopt a method in which a transmitting surface and a reflecting surface are formed from the identical surface by using total reflection (such a reflecting surface will hereinafter be referred to as xe2x80x9ca mutual reflecting surfacexe2x80x9d; a reflecting surface that is not formed from the identical surface with a transmitting surface will hereinafter be referred to as xe2x80x9can independent reflecting surfacexe2x80x9d). In this method, a single surface is arranged to refract light when it is transmitted and to totally reflect light when it is reflected, thereby allowing one and the same surface to function as both transmitting and reflecting surfaces. With this arrangement, the effective portions of the reflecting and transmitting surfaces are permitted to overlap each other. Accordingly, the restrictions on the reflection angle and the reflecting surface separation are relaxed. However, as has been stated above, if a strong power is given to a surface having a large reflection angle, the amount of decentration aberrations produced by this surfaces increases unfavorably. Therefore, a very strong power cannot be given to a mutual reflecting surface, at which the reflection angle cannot be made smaller than the total reflection critical angle (critical angle), and satisfactory aberration correction cannot be effected. Accordingly, the use of a mutual reflecting surface is not always advantageous in terms of performance.
The reason why the performance cannot always be improved even if the number of reflecting surfaces is increased is that the effective portions of reflecting surfaces undesirably overlap each other. Therefore, in order to improve the performance effectively when the number of reflecting surfaces is increased, it is necessary to place reflecting surfaces so that the effective portions thereof do not overlap each other. At the same time, it is necessary to fold the optical axis so as to reduce the size of the optical system. Accordingly, the present invention proposes a compact and high-performance prism optical system attained by appropriately setting the path of rays, that is, optical path, which is determined by the arrangement of reflecting surfaces and the reflection direction.
Let us give a definition of the optical path. When an optical path is folded by a plurality of reflecting surfaces, the optical axis is not always in one plane, but the optical axis may take a three-dimensional optical path, which is not in the same plane. In the prism optical system according to the present invention also, the optical axis may take a three-dimensional optical path. In the following description, the optical path will be defined on a two-dimensional basis such that a three-dimensional optical path is also included.
The optical axis of a decentered optical system is defined by a light ray from the object center that passes through the center of the stop and reaches the center of the image plane. This ray will hereinafter be referred to as xe2x80x9caxial principal rayxe2x80x9d. When a plane is defined by three points at which the axial principal ray impinges on a first transmitting surface, a first reflecting surface and a second reflecting surface placed in order in which light rays pass from the object side, the optical path is defined by the projective axial principal ray, that is, the axial principal ray as projected onto the reference plane. With this definition, a three-dimensional optical path is also included in the scope of the present invention.
Increasing the number of reflections in a prism is favorable from the viewpoint of performance but unfavorable from the viewpoint of size. Thus, the number of reflections relates to both performance and size. In the present invention, therefore, the number of reflections is set at a value with which an increase in performance and a reduction in size can be effectively attained with good balance. If the number of reflections in the prism optical system is two or less, the effect of correcting decentration aberrations is limited, as stated above in regard to the prior art. Therefore, reducing the number of reflections to two or less is unfavorable from the viewpoint of performance. If the number of reflections is increased to four or more, the degree of freedom in the optical path folding direction is reduced, and it becomes difficult to construct the prism optical system in a compact form. In addition, if the number of reflections is increased, the desired prism cannot be constructed unless common reflecting surfaces are used. Thus, increasing the number of reflections is not always favorable for performance. Moreover, if the number of reflections is increased, the effect of manufacturing errors on performance is intensified correspondingly, causing the performance to be degraded unfavorably. Accordingly, the number of reflections is set at three in the prism optical system according to the present invention.
When the optical path of a prism in which there are three reflections is set according to the above-described definition, reflection directions can be divided into two directions, i.e. right and left, with respect to the travel direction of the optical axis. Accordingly, there are 8 different courses that the optical path can take. If symmetric ones are removed from the 8 courses, courses that the optical path can take may be divided into four types as shown in parts (a) to (d) of FIG. 21. To attain a reduction in size, which is an object of the present invention, the optical path needs to be folded in a compact form. In order to achieve high performance, it is necessary to set the optical path so that the effective portion of a transmitting surface and that of a reflecting surface do not overlap each other. Of the four types shown in FIG. 21, the optical path shown in part (a) unavoidably requires the first and third reflecting surfaces to be mutual reflecting surfaces because the effective portions of the transmitting and reflecting surfaces undesirably overlap each other when the light beam is large in size. Consequently, two of the three reflecting surfaces need to be totally reflecting surfaces. This is disadvantageous from the viewpoint of performance. Accordingly, with the optical path shown in part (a) of FIG. 21, the object of the present invention, particularly an improvement in performance, cannot be attained. The optical path shown in part (d) of FIG. 21 is not effectively folded. Accordingly, the size in the direction of the optical axis entering the prism or in a direction perpendicular to the entering optical axis tends to become large, and thus the prism cannot be made compact. Particularly, if each surface is formed from an independent surface, the prism becomes undesirably large in size. For this reason, it is difficult to achieve a reduction in size even if high performance can be attained. Accordingly, with the optical path shown in part (d) of FIG. 21, the object of the present invention, particularly a reduction in size, cannot be attained.
In the optical paths shown in parts (b) and (c) of FIG. 21, on the other hand, the effective portions of the surfaces are unlikely to overlap each other, and it is possible to form each reflecting surface as an independent reflecting surface. This is advantageous from the viewpoint of performance. In addition, the optical path is bent in the same direction at two consecutive reflecting surfaces. Therefore, in the optical path shown in part (b) of FIG. 21, it is possible to reduce the size, particularly the size in the direction of the optical axis entering the prism. In the optical path shown in part (c) of FIG. 21, it is possible to reduce the size, particularly the size in a direction perpendicular to the entering optical axis.
That is, it is possible to attain a reduction in size and an improvement in performance simultaneously, which is the object of the present invention, by taking an optical path that bends at two consecutive reflecting surfaces in the same direction with respect to the travel direction of the rays and bends at the other reflecting surface in a direction different from the direction of bending at the two consecutive reflecting surfaces.
Accordingly, it is preferable to arrange the prism optical system according to the present invention as follows. The prism optical system comprises three reflecting surfaces and has, in order in which light rays pass from the object side, a first transmitting surface, a first reflecting surface, a second reflecting surface, a third reflecting surface, and a second transmitting surface. When the axial principal ray is projected onto a plane defined by three points at which the axial principal ray impinges on the first transmitting surface, the first reflecting surface and the second reflecting surface, the projected axial principal ray forms an optical path that bends at two consecutive reflecting surfaces in the same direction with respect to the direction of travel of the rays and bends at the other reflecting surface in a direction different from the direction of bending at the two reflecting surfaces.
In the above-described optical path, the two consecutive reflecting surfaces, at which the axial principal ray bends in the same direction, should preferably be the first reflecting surface and the second reflecting surface. With this arrangement, it is possible to reduce the size, particularly the size in the direction of the optical axis entering the prism optical system. Therefore, the arrangement is particularly suitable for a finder optical system, an image pickup optical system, etc. of cameras.
In the above-described optical path, it is particularly preferable that the two consecutive reflecting surfaces, at which the axial principal ray bends in the same direction, should be the second reflecting surface and the third reflecting surface. With this arrangement, it is possible to reduce the size, particularly the size in a direction perpendicular to the direction of the entering optical axis. Therefore, the arrangement is particularly suitable for binoculars and the like.
It is possible to attain a reduction in size and an improvement in performance by setting an appropriate optical path using three reflecting surfaces as stated above. However, when the present invention is used in an image-forming optical system, for example, there are cases where satisfactory performance cannot be obtained, depending upon the position of an aperture of the optical system.
In an ordinary refracting optical system or the like, it is easy to place an aperture, e.g. an aperture stop, between lenses. In a prism optical system, however, the prism is filled therein with a medium. Therefore, in order to place an aperture in an intermediate portion of the optical path, it is necessary to divide the prism so that an aperture stop can be placed, or it is necessary to provide the prism with a groove or the like to define an aperture. In the present invention also, the prism can be divided to place an aperture. However, if the prism is divided, performance degradation due to assembling errors is likely to occur. Therefore, division of the prism is unfavorable from the viewpoint of performance. Formation of a groove in the prism to define an aperture is also unfavorable from the viewpoint of performance because there are influences of irregular reflection and scattered light in actual practice. In a case where an aperture is defined by a groove, because the aperture cannot be stopped down physically, another member such as an ND filter is needed, resulting in a rise in cost. Thus, placing an aperture in an intermediate portion of the optical path causes various problems unfavorably.
If an aperture is placed outside the prism, it becomes unnecessary to divide the prism or to form a groove. Accordingly, the above-described problems relating to performance can be solved. Therefore, it is desirable to place the three reflecting surfaces of the prism between the aperture of the optical system and the object plane or between the aperture and the image plane.
As has been stated above, adopting the arrangement of the present invention makes it possible to obtain a prism optical system of high performance despite its compact and thin structure in comparison to the conventional arrangement.
The following is a description of the arrangement of the prism optical system that allows the object of the present invention to be effectively attained.
In the prism optical system according to the present invention, the transmitting surfaces and the reflecting surfaces can be readily formed from surfaces independent of each other by using the above-described optical path. It is also possible in the present invention to form at least one reflecting surface from a mutual reflecting surface. However, using a mutual reflecting surface does not always allow the size of the prism optical system to be reduced to a considerable extent. Performance degradation and reduction in freedom for the exit direction caused by the use of a mutual reflecting surface are greater than the reduction in size. Therefore, it is not preferable to use a mutual reflecting surface. Accordingly, in view of the balance of the size and the performance, it is most desirable to form all the reflecting surfaces independently of the transmitting surfaces.
It is deemed possible to construct the prism in a compact form by making the projected axial principal ray cross itself in the prism to thereby fold the optical path. To the contrary, folding the optical path in a compact form causes the effective portions of the reflecting surfaces to become likely to overlap each other unfavorably. Particularly, when there are three reflecting surfaces as in the present invention, it is necessary to increase the spacing between the reflecting surfaces in order to make them independent reflecting surfaces. This is disadvantageous from the viewpoint of aberration correction. Accordingly, it is preferable to arrange the optical system so that the projected axial principal ray does not cross itself in the prism.
The following is a description of the arrangements of two of the reflecting surfaces at which the projected axial principal ray bends in the same direction consecutively.
In the present invention, a reduction in size is achieved by folding the optical path with two reflecting surfaces at which the projected axial principal ray bends in the same direction consecutively. Therefore, the optical path affects the size of the prism. Accordingly, it is necessary to appropriately set the angle formed between the entrance direction to the two reflecting surfaces and the exit direction therefrom. For this reason, it is preferable to satisfy the following condition:
0xc2x0xe2x89xa6xcex8 less than 45xc2x0xe2x80x83xe2x80x83(1)
where xcex8 is the angle formed between the projected axial principal ray incident on the first reflecting surface of the two reflecting surfaces at which the projected axial principal ray bends in the same direction consecutively and the projected axial principal ray exiting from the second reflecting surface of the two reflecting surfaces. It should be noted that xcex8 is a smaller angle of two angles formed between the projected axial principal ray incident on the first reflecting surface and the projected axial principal ray exiting from the second reflecting surface. Therefore, the angle xcex8 ranges from 0xc2x0 to less than 180xc2x0.
If xcex8 is not smaller than the upper limit of the condition (1), i.e. 45xc2x0, the projected axial principal ray may cross itself undesirably, or the prism becomes undesirably large in size.
It is even more desirable to satisfy the following condition:
0xc2x0xe2x89xa6xcex8 less than 30xc2x0xe2x80x83xe2x80x83(2)
It is preferable from the viewpoint of performance to minimize the reflection angle at a reflecting surface with a power because the smaller the reflection angle, the smaller the amount of decentration aberrations produced by the reflecting surface. However, at two reflecting surfaces at which the projected axial principal ray bends in the same direction consecutively, it is necessary to make the reflection angle relatively large so that the effective portions of the two reflecting surfaces do not overlap the effective portion of another reflecting or transmitting surface. From the viewpoint of performance, however, it is preferable to minimize the reflection angle at at least one of the two reflecting surfaces, at which the projected axial principal ray bends in the same direction consecutively, to thereby minimize the amount of decentration aberrations produced by the reflecting surface. Accordingly, it is preferable that at least one of the two reflecting surfaces should satisfy the following condition:
10xc2x0 less than xcfx861 less than 70xc2x0xe2x80x83xe2x80x83(3)
where xcfx861 is the reflection angle of the axial principal ray at the reflecting surfaces at which the projected axial principal ray bends in the same direction consecutively.
If xcfx861 is not smaller than the upper limit of the condition (3), i.e. 70xc2x0, the amount of decentration aberrations produced by this surface becomes unfavorably large, causing the performance to be degraded. If xcfx861, is not larger than the lower limit, i.e. 10xc2x0, the effective portion of the reflecting surface undesirably overlaps the effective portion of another reflecting or transmitting surface. Consequently, it becomes impossible to construct the desired prism.
It is even more desirable to satisfy the following condition:
20xc2x0 less than xcfx861 less than 60xc2x0xe2x80x83xe2x80x83(4)
As has been stated above, the two reflecting surfaces at which the projected axial principal ray bends in the same direction consecutively need relatively large reflection angles. Therefore, the effective portions of these reflecting surfaces also tend to increase in size. For this reason, to separate the effective portions of the two reflecting surfaces from each other, it is preferable that the spacing between the two reflecting surfaces should satisfy the following condition:
0.1 less than |d/f| less than 3xe2x80x83xe2x80x83(5)
where d is the distance between the two reflecting surfaces along the axial principal ray, and f is the focal length of the entire prism optical system.
If |d/f| is not smaller than the upper limit of the condition (5), i.e. 3, it becomes necessary to increase the optical path length. This causes the prism to become undesirably large in size. If |d/f| is not larger than the lower limit, i.e. 0.1, it becomes difficult to form the reflecting surfaces as independent surfaces.
It is even more desirable to satisfy the following condition:
0.3 less than |d/f| less than 2xe2x80x83xe2x80x83(6)
Regarding the reflecting surface at which the projected axial principal ray bends in a direction different from the direction of bending at the above-described two reflecting surfaces, it is also preferable to minimize the reflection angle at the reflecting surface because the amount of decentration aberrations produced by this surface is reduced by doing so. Accordingly, it is preferable to satisfy the following condition:
20xc2x0 less than xcfx862 less than 70xc2x0xe2x80x83xe2x80x83(7)
where xcfx862 is the reflection angle of the axial principal ray at the reflecting surface at which the projected axial principal ray bends in a direction different from the direction of bending at the two other reflecting surfaces.
If xcfx862 is not smaller than the upper limit of the condition (7), i.e. 70xc2x0, the amount of decentration aberrations produced by this surface becomes unfavorably large, causing the performance to be degraded. If xcfx862 is not larger than the lower limit, i.e. 20xc2x0, the effective portion of the reflecting surface undesirably overlaps the effective portion of another reflecting surface. Consequently, it becomes impossible to construct the desired prism.
It is even more desirable to satisfy the following condition:
30xc2x0 less than xcfx862 less than 60xc2x0xe2x80x83xe2x80x83(8)
Next, the details of the optical path will be described.
In the conventional optical system, the size in the direction of the optical axis entering the optical system, which depends on the focal length and the structural length of the lens, may give rise to a problem. It is deemed that the size of the prism optical system can be reduced because the optical axis is folded. However, when another optical system is connected to the prism optical system or the back focus is long, the size in the direction of the entering optical axis cannot be reduced unless consideration is given to the exit direction from the prism optical system. Therefore, in the prism optical system according to the present invention, it is preferable to set the exit direction of the prism optical system perpendicular to the entrance direction. By doing so, the size in the direction of the entering optical axis does not become large even in the above-described case, and a compact optical system can be obtained. However, there are cases where it is preferable not to set the exit direction completely perpendicular to the entrance direction from the viewpoint of placing another member. Accordingly, it is preferable that the angle formed between the projected axial principal ray entering the prism and the projected axial principal ray exiting from the prism should satisfy the following condition:
45xc2x0 less than xcfx89 less than 135xc2x0xe2x80x83xe2x80x83(9)
where xcfx89 is the angle formed between the projected axial principal ray entering the prism and the projected axial principal ray exiting from the prism. It should be noted that xcfx89 is a smaller angle of two angles formed between the projected axial principal ray entering the prism and the projected axial principal ray exiting from the prism. Therefore, the angle xcfx89 ranges from 0xc2x0 to less than 180xc2x0.
If the angle xcfx89 is not within the range defined by the condition (9), it becomes impossible to reduce the size in the entrance direction of the prism optical system.
It is even more desirable to satisfy the following condition:
60xc2x0 less than xcfx89 less than 120xc2x0xe2x80x83xe2x80x83(10)
In the foregoing, the optical path of the prism optical system is defined by the two-dimensional projected axial principal ray. In the following, a three-dimensional optical path will be described. Even when a reduction in size is achieved by using the optical path of the prism optical system according to the present invention, if the optical path is arranged three-dimensionally, a dead space is likely to occur when the optical system is placed, in general, in comparison to a case where the optical axis lies in one and the same plane. Consequently, a camera or the like that is equipped with the optical system becomes undesirably large in size. Therefore, it is most desirable that the optical path of the prism optical system according to the present invention should lie in one and the same plane. However, there are cases where the optical system becomes compact in size as a whole by using a three-dimensional optical path to place another member. Accordingly, it is preferable that the angle of the axial principal ray exiting from each of the second and third reflecting surfaces to the plane in which the projected axial principal ray is set should satisfy the following conditions:
0xc2x0xe2x89xa6xcex12 less than 30xc2x0xe2x80x83xe2x80x83(11)
0xc2x0xe2x89xa6xcex13 less than 30xc2x0xe2x80x83xe2x80x83(12)
where xcex12 is the angle formed between the plane defined by three points at which the axial principal ray impinges on the first transmitting surface, the first reflecting surface and the second reflecting surface and the axial principal ray exiting from the second reflecting surface, and xcex13 is the angle formed between the plane defined by three points at which the axial principal ray impinges on the first transmitting surface, the first reflecting surface and the second reflecting surface and the axial principal ray exiting from the third reflecting surface. For each of the angles xcex12 and xcex13, a smaller angle of two angles formed with respect to the above-described reference plane is taken. Therefore, the angles xcex12 and xcex13 range from 0xc2x0 to less than 90xc2x0.
If the angles xcex12 and xcex13 are not smaller than the upper limits of the conditions (11) and (12), i.e. 30xc2x0, a dead space occurs, and the optical system becomes undesirably large in size.
It is even more desirable to satisfy the following conditions:
0xc2x0xe2x89xa6xcex12 less than 15xc2x0xe2x80x83xe2x80x83(13)
0xc2x0xe2x89xa6xcex13 less than 15xc2x0xe2x80x83xe2x80x83(14)
If the prism optical system according to the present invention is arranged so that all the surfaces have negative powers, the prism becomes undesirably large in size because the light beam diverges. Accordingly, it is not always possible to attain a reduction in size even if the optical axis is folded by using reflecting surfaces. Therefore, it is preferable to give positive powers to at least two reflecting surfaces.
Furthermore, because the prism optical system according to the present invention has three reflecting surfaces, a loss of light quantity caused by reflection may give rise to a problem. Therefore, at least one of the three reflecting surfaces may be formed into a totally reflecting surface.
Still other objects and advantages of the invention will in part be obvious and will in part be apparent from the specification.
The invention accordingly comprises the features of construction, combinations of elements, and arrangement of parts which will be exemplified in the construction hereinafter set forth, and the scope of the invention will be indicated in the claims.